Question

Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from a random sample and use a 5% significance level Test Ho: p = 0.5 vs Ha : p > 0.5 using the sample results p (hat) = 0.56 with n = 25 Round your answer for the test statistic to two decimal places, and your answer for the p value to three decimal places test statistic = p value = Conclusion reject or accept Ho

Answer 1

Answer:

Given,

Null hypothesis H0: p = 0.5

Alternative hypothesis Ha: p > 0.5 (Right tailed)

Test statistics z = - p / sqrt(p( 1- p) / n)

substitute given values

= 0.56 - 0.50 / sqrt( 0.5 * 0.5 / 25)

= 0.6

Test statistics z = 0.6

Now consider,

p-value = P(Z > z)

= P( Z > 0.6)

= 1 - P( Z< 0.6)

= 1 - 0.7257 [since from standard normal distribution table]

= 0.2743

p-value = 0.2743

Here the p-value is greater than > 0.05 significance level so that we do not have sufficient evidence to reject H0.

Hence we conclude that we fail to reject Ho i.e., null hypothesis.